OVERCONVERGENT REAL CLOSED QUANTIFIER ELIMINATION

Abstract

Let K be the (real closed) field of Puiseux series in t over R endowed with the natural linear order. Then the elements of the formal power series rings R[[ξ1, . . . , ξn]] converge t-adically on [−t, t]n, and hence define functions [−t, t]n → K. Let L be the language of ordered fields, enriched with symbols for these functions. By Corollary 3.17, K is o-minimal in L. This result is obtained from a quantifier elimination theorem. The proofs use methods from non-Archimedean analysis.